Understanding the evolution of local structure and mobility of disordered glassy materials induced by external stress is critical in modeling their mechanical deformation in the nonlinear regime. Several techniques have shown acceleration of molecular mobility of various amorphous glasses under macroscopic tensile deformation, but it remains a major challenge to visualize such a relationship at the nanoscale. Here, we employ a new approach based on atomic force microscopy in nanorheology mode for quantifying the local dynamic responses of a polymer glass induced by nanoscale compression. By increasing the compression level from linear elastic to plastic deformation, we observe an increase in the mechanical loss tangent (tan δ), evidencing the enhancement of polymer mobility induced by large stress. Notably, tan δ images directly reveal the preferential effect of the large compression on the dynamic acceleration of nanoscale heterogeneities with initially slow mobility, which is clearly different from that induced by increasing temperature.